Eintrag weiter verarbeiten
Dynamics of viscous backflow from a model fracture network
Gespeichert in:
| Zeitschriftentitel: | Journal of Fluid Mechanics |
|---|---|
| Personen und Körperschaften: | , , , , , |
| In: | Journal of Fluid Mechanics, 836, 2018, S. 828-849 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Cambridge University Press (CUP)
|
| Schlagwörter: |
| author_facet |
Dana, Asaf Zheng, Zhong Peng, Gunnar G. Stone, Howard A. Huppert, Herbert E. Ramon, Guy Z. Dana, Asaf Zheng, Zhong Peng, Gunnar G. Stone, Howard A. Huppert, Herbert E. Ramon, Guy Z. |
|---|---|
| author |
Dana, Asaf Zheng, Zhong Peng, Gunnar G. Stone, Howard A. Huppert, Herbert E. Ramon, Guy Z. |
| spellingShingle |
Dana, Asaf Zheng, Zhong Peng, Gunnar G. Stone, Howard A. Huppert, Herbert E. Ramon, Guy Z. Journal of Fluid Mechanics Dynamics of viscous backflow from a model fracture network Mechanical Engineering Mechanics of Materials Condensed Matter Physics |
| author_sort |
dana, asaf |
| spelling |
Dana, Asaf Zheng, Zhong Peng, Gunnar G. Stone, Howard A. Huppert, Herbert E. Ramon, Guy Z. 0022-1120 1469-7645 Cambridge University Press (CUP) Mechanical Engineering Mechanics of Materials Condensed Matter Physics http://dx.doi.org/10.1017/jfm.2017.778 <jats:p>Hydraulic fracturing for production of oil and gas from shale formations releases fluid waste, by-products that must be managed carefully to avoid significant harm to human health and the environment. These fluids are presumed to result from a variety of fracture relaxation processes, and are commonly referred to as ‘flowback’ and ‘produced water’, depending primarily on the time scale of their appearance. Here, a model is presented for investigating the dynamics of backflows caused by the elastic relaxation of a pre-strained medium, namely a single fracture and two model fracture network systems: a single bifurcated channel and its generalization for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline1" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula> bifurcated fracture generations. Early- and late-time asymptotic solutions are obtained for the model problems and agree well with numerical solutions. In the late-time period, the fracture apertures and backflow rates exhibit a time dependence of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline2" /><jats:tex-math>$t^{-1/3}$</jats:tex-math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline3" /><jats:tex-math>$t^{-4/3}$</jats:tex-math></jats:alternatives></jats:inline-formula>, respectively. In addition, the pressure distributions collapse to universal curves when scaled by the maximum pressure in the system, which we calculate as a function of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline4" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula>. The pressure gradient along the network is steepest near the outlet while the bulk of the network serves as a ‘reservoir’. Fracture networks with larger <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline5" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula> are less efficient at evicting fluids, manifested through a longer time required for a given fractional reduction of the initial volume. The developed framework may be useful for informing engineering design and environmental regulations.</jats:p> Dynamics of viscous backflow from a model fracture network Journal of Fluid Mechanics |
| doi_str_mv |
10.1017/jfm.2017.778 |
| facet_avail |
Online |
| finc_class_facet |
Technik Physik |
| format |
ElectronicArticle |
| fullrecord |
blob:ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTAxNy9qZm0uMjAxNy43Nzg |
| id |
ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTAxNy9qZm0uMjAxNy43Nzg |
| institution |
DE-D161 DE-Zi4 DE-Gla1 DE-15 DE-Pl11 DE-Rs1 DE-14 DE-105 DE-Ch1 DE-L229 DE-D275 DE-Bn3 DE-Brt1 |
| imprint |
Cambridge University Press (CUP), 2018 |
| imprint_str_mv |
Cambridge University Press (CUP), 2018 |
| issn |
1469-7645 0022-1120 |
| issn_str_mv |
1469-7645 0022-1120 |
| language |
English |
| mega_collection |
Cambridge University Press (CUP) (CrossRef) |
| match_str |
dana2018dynamicsofviscousbackflowfromamodelfracturenetwork |
| publishDateSort |
2018 |
| publisher |
Cambridge University Press (CUP) |
| recordtype |
ai |
| record_format |
ai |
| series |
Journal of Fluid Mechanics |
| source_id |
49 |
| title |
Dynamics of viscous backflow from a model fracture network |
| title_unstemmed |
Dynamics of viscous backflow from a model fracture network |
| title_full |
Dynamics of viscous backflow from a model fracture network |
| title_fullStr |
Dynamics of viscous backflow from a model fracture network |
| title_full_unstemmed |
Dynamics of viscous backflow from a model fracture network |
| title_short |
Dynamics of viscous backflow from a model fracture network |
| title_sort |
dynamics of viscous backflow from a model fracture network |
| topic |
Mechanical Engineering Mechanics of Materials Condensed Matter Physics |
| url |
http://dx.doi.org/10.1017/jfm.2017.778 |
| publishDate |
2018 |
| physical |
828-849 |
| description |
<jats:p>Hydraulic fracturing for production of oil and gas from shale formations releases fluid waste, by-products that must be managed carefully to avoid significant harm to human health and the environment. These fluids are presumed to result from a variety of fracture relaxation processes, and are commonly referred to as ‘flowback’ and ‘produced water’, depending primarily on the time scale of their appearance. Here, a model is presented for investigating the dynamics of backflows caused by the elastic relaxation of a pre-strained medium, namely a single fracture and two model fracture network systems: a single bifurcated channel and its generalization for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline1" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula> bifurcated fracture generations. Early- and late-time asymptotic solutions are obtained for the model problems and agree well with numerical solutions. In the late-time period, the fracture apertures and backflow rates exhibit a time dependence of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline2" /><jats:tex-math>$t^{-1/3}$</jats:tex-math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline3" /><jats:tex-math>$t^{-4/3}$</jats:tex-math></jats:alternatives></jats:inline-formula>, respectively. In addition, the pressure distributions collapse to universal curves when scaled by the maximum pressure in the system, which we calculate as a function of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline4" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula>. The pressure gradient along the network is steepest near the outlet while the bulk of the network serves as a ‘reservoir’. Fracture networks with larger <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline5" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula> are less efficient at evicting fluids, manifested through a longer time required for a given fractional reduction of the initial volume. The developed framework may be useful for informing engineering design and environmental regulations.</jats:p> |
| container_start_page |
828 |
| container_title |
Journal of Fluid Mechanics |
| container_volume |
836 |
| format_de105 |
Article, E-Article |
| format_de14 |
Article, E-Article |
| format_de15 |
Article, E-Article |
| format_de520 |
Article, E-Article |
| format_de540 |
Article, E-Article |
| format_dech1 |
Article, E-Article |
| format_ded117 |
Article, E-Article |
| format_degla1 |
E-Article |
| format_del152 |
Buch |
| format_del189 |
Article, E-Article |
| format_dezi4 |
Article |
| format_dezwi2 |
Article, E-Article |
| format_finc |
Article, E-Article |
| format_nrw |
Article, E-Article |
| _version_ |
1792340288679706624 |
| geogr_code |
not assigned |
| last_indexed |
2024-03-01T16:01:39.186Z |
| geogr_code_person |
not assigned |
| openURL |
url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fvufind.svn.sourceforge.net%3Agenerator&rft.title=Dynamics+of+viscous+backflow+from+a+model+fracture+network&rft.date=2018-02-10&genre=article&issn=1469-7645&volume=836&spage=828&epage=849&pages=828-849&jtitle=Journal+of+Fluid+Mechanics&atitle=Dynamics+of+viscous+backflow+from+a+model+fracture+network&aulast=Ramon&aufirst=Guy+Z.&rft_id=info%3Adoi%2F10.1017%2Fjfm.2017.778&rft.language%5B0%5D=eng |
| SOLR | |
| _version_ | 1792340288679706624 |
| author | Dana, Asaf, Zheng, Zhong, Peng, Gunnar G., Stone, Howard A., Huppert, Herbert E., Ramon, Guy Z. |
| author_facet | Dana, Asaf, Zheng, Zhong, Peng, Gunnar G., Stone, Howard A., Huppert, Herbert E., Ramon, Guy Z., Dana, Asaf, Zheng, Zhong, Peng, Gunnar G., Stone, Howard A., Huppert, Herbert E., Ramon, Guy Z. |
| author_sort | dana, asaf |
| container_start_page | 828 |
| container_title | Journal of Fluid Mechanics |
| container_volume | 836 |
| description | <jats:p>Hydraulic fracturing for production of oil and gas from shale formations releases fluid waste, by-products that must be managed carefully to avoid significant harm to human health and the environment. These fluids are presumed to result from a variety of fracture relaxation processes, and are commonly referred to as ‘flowback’ and ‘produced water’, depending primarily on the time scale of their appearance. Here, a model is presented for investigating the dynamics of backflows caused by the elastic relaxation of a pre-strained medium, namely a single fracture and two model fracture network systems: a single bifurcated channel and its generalization for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline1" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula> bifurcated fracture generations. Early- and late-time asymptotic solutions are obtained for the model problems and agree well with numerical solutions. In the late-time period, the fracture apertures and backflow rates exhibit a time dependence of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline2" /><jats:tex-math>$t^{-1/3}$</jats:tex-math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline3" /><jats:tex-math>$t^{-4/3}$</jats:tex-math></jats:alternatives></jats:inline-formula>, respectively. In addition, the pressure distributions collapse to universal curves when scaled by the maximum pressure in the system, which we calculate as a function of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline4" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula>. The pressure gradient along the network is steepest near the outlet while the bulk of the network serves as a ‘reservoir’. Fracture networks with larger <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline5" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula> are less efficient at evicting fluids, manifested through a longer time required for a given fractional reduction of the initial volume. The developed framework may be useful for informing engineering design and environmental regulations.</jats:p> |
| doi_str_mv | 10.1017/jfm.2017.778 |
| facet_avail | Online |
| finc_class_facet | Technik, Physik |
| format | ElectronicArticle |
| format_de105 | Article, E-Article |
| format_de14 | Article, E-Article |
| format_de15 | Article, E-Article |
| format_de520 | Article, E-Article |
| format_de540 | Article, E-Article |
| format_dech1 | Article, E-Article |
| format_ded117 | Article, E-Article |
| format_degla1 | E-Article |
| format_del152 | Buch |
| format_del189 | Article, E-Article |
| format_dezi4 | Article |
| format_dezwi2 | Article, E-Article |
| format_finc | Article, E-Article |
| format_nrw | Article, E-Article |
| geogr_code | not assigned |
| geogr_code_person | not assigned |
| id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTAxNy9qZm0uMjAxNy43Nzg |
| imprint | Cambridge University Press (CUP), 2018 |
| imprint_str_mv | Cambridge University Press (CUP), 2018 |
| institution | DE-D161, DE-Zi4, DE-Gla1, DE-15, DE-Pl11, DE-Rs1, DE-14, DE-105, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1 |
| issn | 1469-7645, 0022-1120 |
| issn_str_mv | 1469-7645, 0022-1120 |
| language | English |
| last_indexed | 2024-03-01T16:01:39.186Z |
| match_str | dana2018dynamicsofviscousbackflowfromamodelfracturenetwork |
| mega_collection | Cambridge University Press (CUP) (CrossRef) |
| physical | 828-849 |
| publishDate | 2018 |
| publishDateSort | 2018 |
| publisher | Cambridge University Press (CUP) |
| record_format | ai |
| recordtype | ai |
| series | Journal of Fluid Mechanics |
| source_id | 49 |
| spelling | Dana, Asaf Zheng, Zhong Peng, Gunnar G. Stone, Howard A. Huppert, Herbert E. Ramon, Guy Z. 0022-1120 1469-7645 Cambridge University Press (CUP) Mechanical Engineering Mechanics of Materials Condensed Matter Physics http://dx.doi.org/10.1017/jfm.2017.778 <jats:p>Hydraulic fracturing for production of oil and gas from shale formations releases fluid waste, by-products that must be managed carefully to avoid significant harm to human health and the environment. These fluids are presumed to result from a variety of fracture relaxation processes, and are commonly referred to as ‘flowback’ and ‘produced water’, depending primarily on the time scale of their appearance. Here, a model is presented for investigating the dynamics of backflows caused by the elastic relaxation of a pre-strained medium, namely a single fracture and two model fracture network systems: a single bifurcated channel and its generalization for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline1" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula> bifurcated fracture generations. Early- and late-time asymptotic solutions are obtained for the model problems and agree well with numerical solutions. In the late-time period, the fracture apertures and backflow rates exhibit a time dependence of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline2" /><jats:tex-math>$t^{-1/3}$</jats:tex-math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline3" /><jats:tex-math>$t^{-4/3}$</jats:tex-math></jats:alternatives></jats:inline-formula>, respectively. In addition, the pressure distributions collapse to universal curves when scaled by the maximum pressure in the system, which we calculate as a function of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline4" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula>. The pressure gradient along the network is steepest near the outlet while the bulk of the network serves as a ‘reservoir’. Fracture networks with larger <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112017007789_inline5" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula> are less efficient at evicting fluids, manifested through a longer time required for a given fractional reduction of the initial volume. The developed framework may be useful for informing engineering design and environmental regulations.</jats:p> Dynamics of viscous backflow from a model fracture network Journal of Fluid Mechanics |
| spellingShingle | Dana, Asaf, Zheng, Zhong, Peng, Gunnar G., Stone, Howard A., Huppert, Herbert E., Ramon, Guy Z., Journal of Fluid Mechanics, Dynamics of viscous backflow from a model fracture network, Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics |
| title | Dynamics of viscous backflow from a model fracture network |
| title_full | Dynamics of viscous backflow from a model fracture network |
| title_fullStr | Dynamics of viscous backflow from a model fracture network |
| title_full_unstemmed | Dynamics of viscous backflow from a model fracture network |
| title_short | Dynamics of viscous backflow from a model fracture network |
| title_sort | dynamics of viscous backflow from a model fracture network |
| title_unstemmed | Dynamics of viscous backflow from a model fracture network |
| topic | Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics |
| url | http://dx.doi.org/10.1017/jfm.2017.778 |